An Introduction to Riemann-Finsler Geometry

By David Bao, S. Chern, Zhongmin Shen. 2000

2,069 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ee21f31188e18a86ac833368b3407dad49a2d8c2

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In Astronomy and Astrophysics

Citations in the corpus

Uniform convexity and smoothness, and their applications in Finsler geometry (2009, methodology): “We refer to [BCS], [Eg], [Sh1], [Sh2], [Sh3] and [WX] for known results in comparison Finsler geometry.”
On Asymmetric Distances (2013, background): “2 in [1]); indeed it is called a Finslerian Length in Example 2.”
Nonsmooth differential geometry - An approach tailored for spaces with Ricci curvature bounded from below (2014, result): “This notion of gradient is in line with the one used in Finsler geometry, see for instance [19].”
Homogeneous geodesics in homogeneous Finsler spaces (2007, background): “For any vector fields T, V, W on M , we have [2]”
Multiple closed geodesics on bumpy Finsler n-spheres (2007, methodology): “For the definition of closed geodesics on a Finsler manifold, we refer readers to [3] and [28].”
On Null Lagrangians (2005, background): “The geodesics in Finsler geometry may be expressed in two ways [2].”
Covariant formulation of f(Q) theory (2021, background): “[23], this means there is a coordinate system {yμ} in which the affine connection vanishes, Γμν(y ) = 0.”
Gravitational lensing under the effect of Weyl and bumblebee gravities: Applications of Gauss–Bonnet theorem (2018, background): “Optical curvature K can also be rewritten in terms of r [89].”
Finsler interpolation inequalities (2009, methodology): “In this section, we review the fundamentals of Finsler geometry. Basic references are [ 5 ,37].”
The Splitting Theorem in Non-Smooth Context (2013, neutral): “Chapter 6 in [11]) that under general assumptions in a neighborhood of x the function Nx is C 1 and that its differential is given by the formula DNx(y) = Dualy(γ ′ 1), (A.”
Heat flow on Finsler manifolds (2008, methodology): “For further reading and more details, we refer to [BCS] and [Sh3].”
A geometric approach to quantum circuit lower bounds (2005, methodology): “[31] V. V. Shende, S. S. Bullock, and I. L. Markov, arXiv:quant-ph/0406176 (2004).”
Projectively flat Finsler metrics of constant flag curvature (2002, background): “Thus smooth distance functions can be studied using calculus (see [AIM], [BCS]).”